Cylindrical acoustic levitator/concentrator

ABSTRACT

A low-power, inexpensive acoustic apparatus for levitation and/or concentration of aerosols and small liquid/solid samples having particulates up to several millimeters in diameter in air or other fluids is described. It is constructed from a commercially available, hollow cylindrical piezoelectric crystal which has been modified to tune the resonance frequency of the breathing mode resonance of the crystal to that of the interior cavity of the cylinder. When the resonance frequency of the interior cylindrical cavity is matched to the breathing mode resonance of the cylindrical piezoelectric transducer, the acoustic efficiency for establishing a standing wave pattern in the cavity is high. The cylinder does not require accurate alignment of a resonant cavity. Water droplets having diameters greater than 1 mm have been levitated against the force of gravity using less than 1 W of input electrical power. Concentration of aerosol particles in air is also demonstrated.

STATEMENT REGARDING FEDERAL RIGHTS

[0001] This invention was made with government support under ContractNo. W-7405-ENG-36 awarded by the U.S. Department of Energy to TheRegents of The University of California, and in part with support by theDefense Threat Reduction Agency of the Department of Defense. Thegovernment has certain rights in the invention.

FIELD OF THE INVENTION

[0002] The present invention relates generally to acoustic levitationand concentration and, more particularly, to the use of a hollow,cylindrical piezoelectric crystal for levitation and concentration whichrequires only low power and obviates the need for exact alignment ofparts to generate standing waves.

BACKGROUND OF THE INVENTION

[0003] Acoustic levitation provides a means for isolating small samplesof particles having diameters less than several millimeters without theinfluence of a containment vessel (See, e.g., E. H. Trinh, “CompactAcoustic Levitation Device For Studies In Fluid Dynamics And MaterialScience In The Laboratory And Microgravity” Rev. Sci. Instrum. 56,2059-2065 (1985), D. B. Thiessen and P. L. Marston, “Principles Of SomeAcoustical, Electrical, And Optical Manipulation Methods WithApplications To Drops, Bubbles, And Capillary Bridges” ASME Fluids Eng.Div. Publ. FED (1998), M. A. H. Weiser and R. E. Apfel, “Extension OfAcoustic Levitation To Include The Study Of Micron-Size Particles In AMore Compressible Host Liquid” J. Acoust. Soc. Am. 71, 1261-1268 (1982),E. G. Lierke et al., “Acoustic Positioning For Space Processing OfMaterials Science Samples In Mirror Furnaces” in IEEE UltrasonicsSymposium 1129-1139 (1983), K. Yasuda, “Blood Concentration BySuperposition Of Higher Harmonics Of Ultrasound” Jpn. J. Appl. Phys. 36,3130-3135 (1997), Ph. Caperan et al., “Acoustic Agglomeration Of AGlycol For Aerosol: Influence Of Particle Concentration And Intensity OfThe Sound Field At Two Frequencies” J. Aerosol Sci. 26, 595-612 (1995),G. Whitworth et al., “Transport And Harvesting Of Suspended ParticlesUsing Modulated Ultrasound” Ultrasonics 29, 439-444 (1991), and K. M.Martin and 0. A. Ezekoye, “Acoustic Filtration And Sedimentation Of SootParticles” Experiments in Fluids 23, 483-488 (1997)). Most acousticlevitation devices operate by localizing a sample near the nodal planesof an acoustic standing wave. This has proven to be a viable techniquefor measuring material properties of small sample quantities (e.g.droplets, aerosols, etc.) without obscuring the results with the effectsof a mounting apparatus (See, e.g., M. A. H. Weiser and R. E. Apfel,supra, and E. G. Lierke et al., supra). Other applications include theuse of acoustic forces to concentrate aerosols and/or particulates nearthe nodal planes of the field for harvesting or sedimentation purposes.Advances in the design of acoustic levitators over the past severaldecades have proven useful for applications where samples may reside ineither gaseous or liquid host media.

[0004] The standing-wave field produced by an acoustic levitation deviceis strongly dependent upon the spatial alignment of the systemcomponents and often requires moderate to high electrical input powerlevels to drive the acoustic generators and achieve the desiredlevitation. This is especially true for levitating solid and liquidsamples in air. The large acoustic impedance mismatch between thedisplacement-generating device and the air medium is often a difficultproblem to overcome. Resonant transduction devices having Q>1000 havebeen built to address this problem and have proven quite useful whenelectrical power efficiency is not a limiting factor (See, e.g., D. B.Thiessen and P. L. Marston, supra, and J. A. Gallego Juarez and G.Rodriguez Corral “Piezoelectric Transducer For Air-Borne Ultrasound”Acustica 29, 234-239 (1973)).

[0005] Piezoelectric cylinders have received significant attention byindustry. Such crystals are used for vibration damping, sources forsonar, sensors and actuators, motors and X-Y micropositioners, to nameseveral uses.

[0006] Accordingly, it is an object of the present invention to providean apparatus for efficiently achieving acoustic levitation andconcentration which in its simplest embodiment is free from therequirement of careful alignment of its component members.

[0007] Additional objects, advantages and novel features of theinvention will be set forth, in part, in the description that follows,and, in part, will become apparent to those skilled in the art uponexamination of the following or may be learned by practice of theinvention. The objects and advantages of the invention may be realizedand attained by means of the instrumentalities and combinationsparticularly pointed out in the appended claims.

SUMMARY OF THE INVENTION

[0008] To achieve the foregoing and other objects of the presentinvention, and in accordance with its purposes, as embodied and broadlydescribed herein, the method for concentrating particles suspended in afluid hereof includes the steps of: matching the breathing-mode acousticresonance of a hollow cylindrical piezoelectric transducer to theacoustic resonance of the interior volume thereof when filled with thefluid; applying periodic electrical excitation thereto such thatresonant acoustic waves are generated in the interior volume of thecylindrical piezoelectric transducer; and subjecting the fluid havingparticles suspended therein to the equilibrium force pattern formed bythe resonant acoustic waves such that the particles move to the regionof the equilibrium force pattern and are concentrated thereby.

[0009] It is preferred that the step of matching the breathing-modeacoustic resonance of the cylindrical piezoelectric transducer to theacoustic resonance of the interior thereof when filled with the fluid isachieved by inserting a cylindrical-shaped rod into the piezoelectriccylinder such that the axis of the cylindrical-shaped rod is collinearwith the axis of the piezoelectric cylinder.

[0010] Preferably, the length of the cylindrical-shaped rod isapproximately the length of the cylindrical piezoelectric transducer andthe diameter of the rod is chosen such that the length of the annularspace between the cylindrical rod and the hollow cylindricalpiezoelectric transducer along a radius thereof is an integral number ofhalf-wavelengths of sound in the fluid inside of the annular space atthe resonant frequency of the piezoelectric transducer.

[0011] In another aspect of the present invention in accordance with itsobjects and purposes the method for levitating particles in a fluidhereof includes the steps of: matching the breathing-mode acousticresonance of a hollow, cylindrical piezoelectric transducer to theacoustic resonance of the interior thereof when filled with the fluid;applying periodic electrical excitation to the surface of thecylindrical piezoelectric transducer such that resonant acoustic wavesare generated in the interior of the cylindrical piezoelectrictransducer; and subjecting the particles to the equilibrium forcepattern formed by the resonant acoustic waves such that the particlesare levitated by the equilibrium force pattern.

[0012] Preferably the step of matching the breathing-mode acousticresonance of a cylindrical piezoelectric transducer to the acousticresonance of the interior thereof when filled with the fluid is achievedby inserting a cylindrical-shaped rod into the piezoelectric cylindersuch that the axis of the cylindrical-shaped rod is collinear with theaxis of the piezoelectric cylinder.

[0013] It is preferred that the length of the cylindrical-shaped rod isapproximately the length of the cylindrical piezoelectric transducer andthat the diameter of the rod is chosen such that the length of theannular space between the cylindrical insert and the hollow cylindricalpiezoelectric transducer along a radius thereof is an integral number ofhalf-wavelengths of sound in the fluid inside of the annular space atthe resonant frequency of the cylindrical piezoelectric transducer.

[0014] Preferably also the fluid includes air.

[0015] In yet a further aspect of the present invention, in accordancewith its objects and purposes the apparatus for concentrating particlessuspended or entrained in a fluid hereof includes in combination: acylindrical piezoelectric transducer having a hollow interior portionand wherein the breathing-mode acoustic resonance of the cylindricalpiezoelectric transducer is matched to the acoustic resonance of theinterior portion thereof when the interior portion is filled with thefluid; a function generator for applying periodic electrical excitationto the surface of the cylindrical piezoelectric transducer such thatresonant acoustic waves in are generated in the hollow interior portionof the cylindrical piezoelectric transducer; and means for introducingthe fluid having particles suspended or entrained therein into theregion of the equilibrium force pattern formed by the resonant acousticwaves such that the particles move to the region of the equilibriumforce pattern and are concentrated thereby.

[0016] Preferably, the apparatus includes a cylindrical-shaped roddisposed in the interior portion of said piezoelectric cylinder suchthat the axis of the cylindrical-shaped rod is collinear with the axisof the piezoelectric cylinder and forming thereby an annular region,whereby the breathing-mode acoustic resonance of the cylindricalpiezoelectric transducer is matched to the acoustic resonance of theinterior portion thereof when filled with said fluid.

[0017] It is preferred that the length of said cylindrical-shaped rod isapproximately the length of the cylindrical piezoelectric transducer andthat the diameter of the rod is chosen such that the length of theannular space between the cylindrical rod and the hollow cylindricalpiezoelectric transducer along a radius thereof is an integral number ofhalf-wavelengths of sound in the fluid inside of the annular space atthe resonant frequency of the cylindrical piezoelectric transducer.

[0018] It is also preferred that the diameter of the cylindrical-shapedrod is twice the wavelength of sound within the fluid inside of theannular space at the resonant frequency of the piezoelectric transducer,whereby a single equilibrium force pattern is generated within theannular region.

[0019] In still another aspect of the invention in accordance with itsobjects and purposes the apparatus for levitating particles in a fluidhereof includes: a cylindrical piezoelectric transducer having a hollowinterior portion such that the breathing-mode acoustic resonance thereofis matched to the acoustic resonance of the hollow interior portionthereof when filled with the fluid; a function generator for applyingperiodic electrical excitation to the surface of the cylindricalpiezoelectric transducer whereby resonant acoustic waves are generatedin the hollow interior portion of the cylindrical piezoelectrictransducer; and means for introducing the particles into the equilibriumforce pattern formed by the resonant acoustic waves such that theparticles are suspended by the equilibrium force pattern.

[0020] Preferably, the apparatus includes a cylindrical-shaped roddisposed in the hollow interior portion of the piezoelectric cylindersuch that the axis of the cylindrical-shaped rod is collinear with theaxis of the piezoelectric cylinder forming thereby an annular region,whereby the breathing-mode acoustic resonance of the cylindricalpiezoelectric transducer is matched with the acoustic resonance of theinterior thereof when filled with the fluid.

[0021] It is preferred that the length of the cylindrical-shaped rod isapproximately the length of the cylindrical piezoelectric transducer andthat the diameter of the cylindrical-shaped rod is chosen such that thelength of the annular region between the cylindrical insert and thehollow cylindrical piezoelectric transducer along a radius thereof is anintegral number of half-wavelengths of sound in the fluid inside of theannular region at the resonant frequency of the cylindricalpiezoelectric transducer.

[0022] Benefits and advantages of the present invention include lowpower operation, the commercial availability of hollow piezoelectriccylinders in numerous materials and sizes and freedom from exactingalignment requirements for component parts.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The accompanying drawings, which are incorporated in and form apart of the specification, illustrate the embodiments of the presentinvention and, together with the description, serve to explain theprinciples of the invention. In the drawings:

[0024]FIG. 1a is a schematic representation of a perspective view of thehollow piezoelectric cylinder of the present invention, showing theouter and inner electrode structures which permit electric power to beapplied to the cylinder, while FIG. 1b is a side view thereof.

[0025]FIG. 2 is a schematic representation of a perspective view of thehollow PZT cylinder shown in FIG. 1 hereof illustrating the axial cutmade in the wall of the cylinder for the purpose of tuning the breathingmode frequency of the cylinder to match a resonant mode of thefluid-filled interior of the cylinder.

[0026]FIG. 3a is a graph of the normalized, time-averaged forceexperienced by a spherical water droplet in a cylindrical cavity havingthe same dimension as used in the demonstration of the apparatus of thepresent invention as a function of the distance from the cylinder axis,where the arrows correspond to the direction of the force and the blackcircles denote the stable equilibrium positions, while FIG. 3b is aschematic representation of the interior cavity of the cylindricallevitator/concentrator, where the dotted lines denote the stableequilibrium positions labeled A, B and C.

[0027]FIG. 4 is a graph of the particle concentration profile as afunction of the distance from any of the equilibrium positions.

[0028]FIG. 5a is a schematic representation of the top view of a secondembodiment of the particle concentrator of the present invention whereina cylindrical insert is disposed along the axis of the piezoelectriccylinder which has the effect of altering the three equilibrium modepattern illustrated in FIG. 3b hereof to that of a single-mode pattern,while FIG. 5b is a schematic representation of a perspective viewthereof.

[0029]FIG. 6a is a schematic representation of the top view of a thirdembodiment of the particle concentrator of the present invention whereinan elliptical insert is disposed along the axis of the piezoelectriccylinder which has the effect of altering the three equilibrium modepattern illustrated in FIG. 3b hereof to that of two tubular patterns,while FIG. 6b is a schematic representation of a perspective viewthereof.

[0030]FIG. 7a is a schematic representation of the top view of theapparatus illustrated in FIG. 6a hereof with the cylindrical insertthereof being replaced by an axially disposed cylindrical piezoelectrictransducer and the outer piezoelectric transducer being replaced by asemi-rigid cylindrical pipe, while FIG. 7b is a schematic representationof a perspective view thereof.

[0031]FIG. 8 is a graph of the particle count as a function of time forthe apparatus shown in FIGS. 6a and 6 b hereof showing the increase anddecrease of particle reaching a detector as the acoustic energy isrepeatedly turned on and turned off, respectively.

DETAILED DESCRIPTION

[0032] Briefly, the present invention includes an apparatus for acousticlevitation and/or concentration of samples in fluids such as air. It isconstructed from a commercially available, hollow cylindricalpiezoelectric crystal which has been modified to tune the resonancefrequency of the breathing mode resonance of the crystal to that of theinterior cavity of the cylinder. When the resonance frequency of theinterior cylindrical cavity is matched to the breathing mode resonanceof the cylindrical piezoelectric transducer, the acoustic efficiency forestablishing a standing wave pattern in the cavity is high.

[0033] Reference will now be made in detail to the present preferredembodiments of the invention examples of which are illustrated in theaccompanying drawings. Same or similar structure is identified usingidentical callouts. Turning now to the drawings, a diagram of thecylindrical levitator used to verify the teachings of the presentinvention is displayed in FIGS. 1a and 1 b. Piezoelectric cylindricalshell, 10, having an inner diameter 16.9 mm, outer diameter 19.0, andlength 17.0 mm was purchased from the Valpey-Fisher Corporation,Hopkinton, Mass. 01748 (VP-A55). The cylinder is radially poled withinner, 12, and outer, 14, nickel surface electrodes (silver has alsobeen used) which are placed in electrical connection with functiongenerator (oscillator), 16, which may include an amplifier if required.Typically, such cylinders are available from several manufacturers andin a plurality of dimensions and materials. Moreover, the direction ofvibration of the cylindrical surface when stimulated using an electricsine-wave signal is determined by the direction of polarization.Although the cylinder used to demonstrate the present invention wasfabricated from lead zirconate/lead titanate (PZT) and was poled(direction of polarization) in the radial direction at the factory, thepresent invention is not limited to such polarization nor is it limitedto the use of PZT. Axial poling will also provide the desiredbreathing-mode vibrations of the hollow cylinder, since changes in theaxial direction also affects the radial dimensions of the cylinder dueto the finite Poisson ratio of the material. It should also be mentionedthat electrical excitation of the piezoelectric transducer need not besinusoidal in nature. Periodic electrical excitation having otherwaveforms would provide the appropriate excitation signal for thepiezoelectric transducers of the present invention.

[0034] As stated hereinabove, it is necessary to match the frequency ofthe breathing-mode resonance of the cylindrical shell to the resonancefrequency of the interior fluid-filled cavity. Measurements of theradial velocity using a commercial Doppler laser vibrometer demonstratethat a stock VP-A55 cylinder having the dimensions set forth hereinabovehas two peaks and corresponding minima in the measured impedance, andthe cylinder has an appreciable radial vibration amplitude in theregions about the impedance minima (near 59 kHz and 61 kHz at 20° C.).These minima are accompanied by a zero value of phase and the tworesonance peaks in the impedance occur near the manufacturer's predictedvalue for the lowest-order radial mode (breathing mode). The resonancefrequency of the interior of the cavity when filled with air as theoperating fluid may be calculated from the Equation for U(r) set forthhereinabove using a value c_(air)=343 m/s at 20° C. is 65.54 kHz. It istherefore necessary to tune the resonance frequency of the piezoelectriccylinder such that it matches the resonance frequency of the cavity.

[0035] Three procedures may be employed to accomplish this tuning.First, the resonance frequency of cylinder 10 can be tuned by cutting anaxial slice, 18, out of the wall of cylinder 10 as shown in FIG. 2hereof. Slice 18 having a width of approximately 0.50 mm, was made usinga rotary diamond saw and was observed to shift the resonance frequencyof the piezoelectric cylinder by 5-7 kHz to a single resonance peakwhich is approximately the resonance frequency of air-filled cavity, 20.Measurements made using a laser vibrometer demonstrate no appreciablechange in the radial vibration amplitude of the cylinder except in thevicinity of the slice where there is a marked decrease in vibrationamplitude. It should be mentioned that a simple cut in the cylindermaterial parallel to the axis of the cylinder was also found to generateapproximately the same shift in frequency.

[0036] Subsequent to the tuning procedure described hereinabove, it wasfound that the piezoelectric material composition of the cylinder couldbe selected to achieve the desired breathing-mode resonance frequencywithout having to physically alter the cylinder. As will be describedhereinbelow, the cavity resonance can be tuned by placing an inserthaving appropriate dimensions into the cavity.

[0037] Although no mention is made as to how to generate such a field,M. Barmatz and P. Collas in “Acoustic Radiation Potential On A Sphere InPlane, Cylindrical, And Spherical Standing Wave Fields”, J. Acoust. Soc.Am. 77, 928-945 (1985)) disclose an expression for the radiationpotential U of the acoustic force on a small spherical particle in acylindrical standing-wave field. For axisymmetric normal modes, thepotential may be written${{U(r)} = \frac{\left( {{\frac{Y_{1}}{3}{J_{0}^{2}\left( {k\quad r} \right)}} - {\frac{Y_{2}}{2}{J_{1}^{2}\left( {k\quad r} \right)}}} \right)}{\pi \quad R^{3}{\rho\upsilon}_{0}^{3}}},$

[0038] , where${Y_{1} = {1 - \frac{\rho \quad c^{2}}{\rho_{p}c_{p}^{2}}}},{{{and}\quad Y_{2}} = {\frac{2\left( {\rho_{p} - \rho} \right)}{\left( {{2\rho_{p}} + \rho} \right)}.}}$

[0039] Here c is the compressional velocity in air, ρ is the airdensity, c_(p) is the compressional velocity of the particle, ρ_(p) isthe particle density, ν_(p) is the maximum particle velocity, and J_(n)is a Bessel function of the first kind. The compressional wave number inair is k=2πf/c and r is the radial coordinate. For a cavity having rigidwalls and inner radius R, the normal mode resonance frequencies aref_(n)=cX_(n)/(2πR), where X_(n) is the nth zero of J₁(X_(n))=0.

[0040] For the present application, the cavity resonance correspondingto n=3 applies to the hollow PZT cylinder. A plot of the time-averagedradial force on a particle in the cavity, F=−dU/dr, is shown in FIG. 3a.The parameters used in the calculation correspond to a water droplet inair. The n=3 resonance condition possesses three stable equilibriumpositions denoted by solid circles in the figure, where the net force iszero and restoring forces act in the direction of the equilibriumposition. The restoring forces weaken as the distance from the center ofthe cavity increases. In the absence of other forces, these equilibriumpositions define three concentric cylindrical surfaces in thecylindrical cavity. A cross section of these surfaces is shown in FIG.3b. It should be noted that although the resonance frequency of thecavity is calculated assuming a rigid-walled cavity, measurementsdemonstrate that this model is a good approximation for the presentinvention.

[0041] If cylinder 10 is oriented such that the cylinder axis isapproximately horizontal such that the force of gravity is directedradially, an oblate spheroid drop of water (major diameter 0.92 mm,minor diameter 0.55 mm) having a mass of 0.243 mg has been levitatedwith a measured input electrical power of approximately 115 mW(2.39×10⁻⁶ N) using a 66.7 kHz sinusoid excitation frequency in theinnermost pressure node ring of the cylinder (The ring marked “C” inFIG. 3b). Due to the low power requirements of the PZT cylinder it isdriven directly from a function generator without the need for a poweramplifier. The ambient temperature for this measurements wasapproximately 27° C. Because of the force pattern in the cavity, smalldroplets introduced into the cavity as a fine mist accumulate in theregions of force equilibrium and agglomerate to form visible dropletswhich are studied. Since both the resonance frequency of the crystal andthe resonance frequency of the air-filled cavity are temperaturedependent, resonance frequencies will vary slightly depending on thelocal temperature. It should be mentioned that other fine particlesentrained or suspended in fluids are likely to coagulate in the regionsof force equilibrium when introduced into the cylindrical PZT.

[0042] It has been observed that a finite restoring force also existsalong the cylinder axis acting along the axis in the direction ofmidpoint of the cylinder. As a result of this force (most likely due tothe finite length of the cylinder) the cavity exhibits a stableequilibrium position with appropriate restoring forces acting along thecylinder axis.

[0043] Visual inspection of the nodal pattern of the pressure field hasbeen accomplished by introducing a small amount of water vapor into thecavity and observing the scattered light from the water droplets formedusing Schlieren techniques when a diffuse white light illuminates theinterior cylindrical cavity. The two innermost rings are readilydiscernable. More difficult to observe is the outermost ring which isvisible in various locations near the interior wall of the device. Theapplied sinusoidal voltage necessary to concentrate the aerosol into thenodal rings has been observed to be less than 1.0 V_(pp). Thus, thepresent apparatus both levitates and concentrates water droplets.

[0044] The breathing mode resonance of the cylinder has a measuredquality factor, Q˜100. As the temperature of the air in the cavitychanges, the cavity resonance is expected change accordingly. To testthe cavity stability, a standard spherical sample (mass=2.54 mg anddiameter=1.4 mm) was levitated in the outermost ring of the cavity(labeled “A” in FIG. 3(b)). The drive amplitude was then lowered untilthe acoustic lifting force no longer exceeds the gravitational force onthe water droplet and the droplet falls. The voltage and current weremeasured as a function of temperature and frequency of the drive signal.The driving frequency was found to vary between 66.1 kHz and 68.3 kHz asthe temperature was increased from 20° C. to 50° C.

[0045]FIG. 4 is a graph of the particle concentration profile as afunction of the distance from any of the equilibrium positions. Thespread is inversely proportional to the particle density.

[0046]FIG. 5a is a schematic representation of the top view of anotherembodiment of the particle concentrator of the present invention, whileFIG. 5b is a schematic representation of a perspective view thereof.Solid rod, 22, having a circular cross section, is located within cavity20 of cylindrical resonator 10 collinear with the axis thereof by meansof supports, 24, to allow tuning of the acoustic cavity. The length ofthe cylindrical insert is approximately the length of the cylindricalpiezoelectric transducer. By changing the rod diameter, it is possibleto shift the resonance frequency of the cavity. The diameter of the rodis chosen such that the length of the annular space between thecylindrical insert and the hollow cylindrical PZT along a radius thereofis an integral number of half-wavelengths of sound in the fluid insideof the annular space. Moreover, in order to generate but a single nodewithin the annular region, the diameter of the cylindrical rod must betwice the wavelength of sound within the fluid inside of the annularspace. Returning to the dotted portion of FIG. 3a, it is seen that theinsertion of a rod results in the creation of a single force equilibriumnode having a greater strength than those of any of A, B, or C shown inFIG. 3b. Means, 26, are provided for introducing a fluid, 28, containingparticles, into cylinder 10. For example, a fan is utilized in the caseof particulate-bearing air. In operation, the acoustic forces causeparticles present in the cavity to collect near nodal plane, 30, asshown in the figure. The nodal plane is in the shape of a cylindricalsheet which extends the length of the cavity. Circular collector, 32, isplaced directly under the nodal plane. In actuality, in order toseparate the fluid from the particles, collector 32 comprises aplurality of hollow collectors (in the case illustrated, four), 34 a-34d having one open end thereof, 36, in the vicinity of the nodal plane.Means, 38, for removing the fluid from piezoelectric cylinder 10 and forcollecting the separated particles, 40, are also provided. In the caseof particulate-bearing air, a fan can be used in this position in placeof a fan as means 26. Thus, as the fluid enters the top of the apparatusand flows through the cavity particulates are forced to positions nearthe nodal line. Upon reaching the collector, the particulates areseparated from the fluid stream with the main air stream being ejectedfrom the device.

[0047]FIG. 6a is a schematic representation of the top view of a thirdembodiment of the particle concentrator of the present invention, whileFIG. 6b is a schematic representation of a perspective view thereof.Here, circular cross-section tuning rod 22 shown in FIGS. 5a and 5 b isreplaced with a rod having an elliptical cross section and having itscentral axis along that for piezoelectric cylinder 10. This changes thespatial response of the cavity such that the particles collect near twonodal circles, 42 a and 42 b. The collectors, 44 a and 44 b, are now inthe shape of small ‘straws’. Otherwise, this embodiment operates in asimilar manner to that illustrated in FIGS. 5a and 5 b hereof.

[0048]FIG. 7a is a schematic representation of the top view of theapparatus illustrated in FIG. 6a hereof where the elliptical insert 22has been replaced by axially disposed elliptical piezoelectrictransducer, 46, and the outer piezoelectric transducer is replaced byrigid cylindrical pipe, 48, while FIG. 7b is a schematic representationof a perspective view thereof. This embodiment operates in a similarmanner to that for the embodiment illustrated in FIGS. 6a and 6 bhereof. Likewise, replacing cylindrical insert 22 in FIGS. 5a and 5 bwith a cylindrical piezoelectric transducer and cylindricalpiezoelectric transducer 10 with a rigid cylinder, would generate anapparatus which operates in a similar manner to the apparatusillustrated in FIGS. 5a and 5 b.

[0049]FIG. 8 is a graph of the particle count as a function of time forthe apparatus shown in FIGS. 6a and 6 b hereof showing the increase anddecrease of particle reaching a detector as the acoustic energy isrepeatedly turned on and turned off, respectively. The fluid employedwas air and the suspended particulates were dust particles. Thecommercial particle sizer was adjusted to view approximately 0.5 μmparticles.

[0050] The foregoing description of the invention has been presented forpurposes of illustration and description and is not intended to beexhaustive or to limit the invention to the precise form disclosed, andobviously many modifications and variations are possible in light of theabove teaching. The embodiments were chosen and described in order tobest explain the principles of the invention and its practicalapplication to thereby enable others skilled in the art to best utilizethe invention in various embodiments and with various modifications asare suited to the particular use contemplated. It is intended that thescope of the invention be defined by the claims appended hereto.

What is claimed is:
 1. A method for concentrating particles suspended orentrained in a fluid which comprises the steps of: (a) matching thebreathing-mode acoustic resonance of a hollow, cylindrical piezoelectrictransducer to the acoustic resonance of the hollow interior thereof whenfilled with said fluid; (b) applying periodic electrical excitation tothe surface of the cylindrical piezoelectric transducer such thatresonant acoustic waves are generated in the interior of the cylindricalpiezoelectric transducer; and (c) subjecting the fluid having particlessuspended or entrained therein to the equilibrium force pattern formedby the resonant acoustic waves such that the particles move to theregion of the equilibrium force pattern and are concentrated thereby. 2.The method as described in claim 1, wherein said step of matching thebreathing-mode acoustic resonance of a cylindrical piezoelectrictransducer to the acoustic resonance of the interior thereof when filledwith said fluid is achieved by inserting a cylindrical-shaped rod intothe piezoelectric cylinder such that the axis of the cylindrical-shapedrod is collinear with the axis of the piezoelectric cylinder.
 3. Themethod as described in claim 2, wherein the length of thecylindrical-shaped rod is approximately the length of the cylindricalpiezoelectric transducer and wherein the diameter of the rod is chosensuch that the length of the annular space between the cylindrical rodand the hollow cylindrical piezoelectric transducer along a radiusthereof is an integral number of half-wavelengths of sound in said fluidinside of the annular space at the resonant frequency of the cylindricalpiezoelectric transducer.
 4. The method as described in claim 3, whereinthe diameter of the cylindrical-shaped rod is twice the wavelength ofsound within said fluid inside of the annular space at the resonantfrequency of the piezoelectric transducer, whereby a single equilibriumforce pattern is generated within the annular region.
 5. The method asdescribed in claim 1; wherein said step of matching the breathing-modeacoustic resonance of a cylindrical piezoelectric transducer to theacoustic resonance of the interior thereof when filled with said fluidis achieved by inserting an elliptical-shaped rod into the piezoelectriccylinder such that the axis of the center of the elliptical-shaped rodis collinear with the axis of the piezoelectric cylinder.
 6. The methodas described in claim 5, wherein the length of the elliptical-shaped rodis approximately the length of the cylindrical piezoelectric transducer.7. The method as described in claim 1, further comprising the step offlowing said fluid having particles suspended or entrained thereinthrough the cylindrical piezoelectric transducer.
 8. The method asdescribed in claim 1, further comprising the step of separating theconcentrated particles from said fluid having particles suspended orentrained therein.
 9. The method as described in claim 1, wherein saidfluid comprises air.
 10. A method for levitating particles in a fluidwhich comprises the steps of: (a) matching the breathing-mode acousticresonance of a hollow, cylindrical piezoelectric transducer to theacoustic resonance of the interior thereof when filled with said fluid;(b) applying periodic electrical excitation to the surface of thecylindrical piezoelectric transducer such that resonant acoustic wavesare generated in the interior of the cylindrical piezoelectrictransducer; and (c) subjecting the particles to the equilibrium forcepattern formed by the resonant acoustic waves such that the particlesare suspended by the equilibrium force pattern.
 11. The method asdescribed in claim 10, wherein said step of matching the breathing-modeacoustic resonance of a cylindrical piezoelectric transducer to theacoustic resonance of the interior thereof when filled with said fluidis achieved by inserting a cylindrical-shaped rod into the piezoelectriccylinder such that the axis of the cylindrical-shaped rod is collinearwith the axis of the piezoelectric cylinder.
 12. The method as describedin claim 11, wherein the length of the cylindrical-shaped rod isapproximately the length of the cylindrical piezoelectric transducer andwherein the diameter of the rod is chosen such that the length of theannular space between the cylindrical rod and the hollow cylindricalpiezoelectric transducer along a radius thereof is an integral number ofhalf-wavelengths of sound in said fluid inside of the annular space atthe resonant frequency of the cylindrical piezoelectric transducer. 13.The method as described in claim 10, wherein said fluid comprises air.14. An apparatus for concentrating particles suspended or entrained in afluid which comprises in combination: (a) a cylindrical piezoelectrictransducer having a hollow interior portion and wherein thebreathing-mode acoustic resonance of said cylindrical piezoelectrictransducer is matched to the acoustic resonance of the interior portionthereof when the interior portion is filled with said fluid; (b) afunction generator for applying periodic electrical excitation to thesurface of said cylindrical piezoelectric transducer such that resonantacoustic waves in are generated in the hollow interior portion of thecylindrical piezoelectric transducer; and (c) means for introducing thefluid having particles suspended or entrained therein into the region ofthe equilibrium force pattern formed by the resonant acoustic waves suchthat the particles move to the region of the equilibrium force patternand are concentrated thereby.
 15. The apparatus as described in claim14, further comprising a cylindrical-shaped rod disposed in the interiorportion of said piezoelectric cylinder such that the axis of saidcylindrical-shaped rod is collinear with the axis of said piezoelectriccylinder forming thereby an annular region, whereby the breathing-modeacoustic resonance of said cylindrical piezoelectric transducer ismatched to the acoustic resonance of the interior portion thereof whenfilled with said fluid.
 16. The apparatus as described in claim 15,wherein the length of said cylindrical-shaped rod is approximately thelength of said cylindrical piezoelectric transducer and wherein thediameter of the rod is chosen such that the length of the annular spacebetween said cylindrical rod and said hollow cylindrical piezoelectrictransducer along a radius thereof is an integral number ofhalf-wavelengths of sound in said fluid inside of the annular space atthe resonant frequency of said cylindrical piezoelectric transducer. 17.The apparatus as described in claim 16, wherein the diameter of saidcylindrical-shaped rod is twice the wavelength of sound within saidfluid inside of the annular space at the resonant frequency of saidpiezoelectric transducer, whereby a single equilibrium force pattern isgenerated within the annular region.
 18. The apparatus as described inclaim 14, further comprising an elliptical-shaped rod disposed in thehollow interior portion of said piezoelectric cylinder such that theaxis of the center of said elliptical-shaped rod is collinear with theaxis of said piezoelectric cylinder, whereby the breathing-mode acousticresonance of said cylindrical piezoelectric transducer is matched to theacoustic resonance of the hollow interior portion thereof when filledwith said fluid.
 19. The apparatus as described in claim 18, wherein thelength of said elliptical-shaped rod is approximately the length of saidcylindrical piezoelectric transducer.
 20. The apparatus as described inclaim 14, further comprising means for flowing said fluid havingparticles suspended or entrained therein through said cylindricalpiezoelectric transducer.
 21. The apparatus as described in claim 14,further comprising means for separating the concentrated particles fromsaid fluid having particles suspended or entrained therein.
 22. Theapparatus as described in claim 14, wherein said fluid comprises air.23. An apparatus for levitating particles in a fluid which comprises incombination: (a) a cylindrical piezoelectric transducer having a hollowinterior portion such that the breathing-mode acoustic resonance thereofis matched to the acoustic resonance of the hollow interior portionthereof when filled with said fluid; (b) a function generator forapplying periodic electrical excitation to the surface of saidcylindrical piezoelectric transducer whereby resonant acoustic waves aregenerated in the hollow interior portion of said cylindricalpiezoelectric transducer; and (c) means for introducing the particlesinto the equilibrium force pattern formed by the resonant acoustic wavessuch that the particles are suspended by the equilibrium force pattern.24. The apparatus as described in claim 23, further comprising acylindrical-shaped rod disposed in the hollow interior portion of saidpiezoelectric cylinder such that the axis of said cylindrical-shaped rodis collinear with the axis of said piezoelectric cylinder formingthereby an annular region, whereby the breathing-mode acoustic resonanceof said cylindrical piezoelectric transducer is matched with theacoustic resonance of the interior thereof when filled with said fluid.25. The apparatus as described in claim 24, wherein the length of saidcylindrical-shaped rod is approximately the length of said cylindricalpiezoelectric transducer and wherein the diameter of saidcylindrical-shaped rod is chosen such that the length of the annularregion between said cylindrical insert and said hollow cylindricalpiezoelectric transducer along a radius thereof is an integral number ofhalf-wavelengths of sound in said fluid inside of the annular region atthe resonant frequency of said cylindrical piezoelectric transducer. 26.The apparatus as described in claim 23, wherein said fluid comprisesair.
 27. A method for concentrating particles suspended or entrained ina fluid which comprises the steps of: (a) matching the breathing-modeacoustic resonance of a hollow, cylindrical piezoelectric transducer tothe acoustic resonance of the volume formed between the cylindricalpiezoelectric transducer and a rigid cylinder surrounding thecylindrical piezoelectric transducer and coaxial thereto when the volumeis filled with said fluid; (b) applying periodic electrical excitationto the surface of the cylindrical piezoelectric transducer such thatresonant acoustic waves are generated in the volume between thecylindrical piezoelectric transducer and the rigid cylinder; and (c)subjecting the fluid having particles suspended or entrained therein tothe equilibrium force pattern formed by the resonant acoustic waves suchthat the particles move to the region of the equilibrium force patternand are concentrated thereby.
 28. An apparatus for concentratingparticles suspended or entrained in a fluid which comprises incombination: (a) a hollow, cylindrical piezoelectric transducer; (b) arigid cylinder surrounding said cylindrical piezoelectric transducer andcoaxial thereto, forming a volume therebetween such that thebreathing-mode acoustic resonance of said cylindrical piezoelectrictransducer is matched to the acoustic resonance of the volume when thevolume is filled with said fluid; (c) a function generator for applyingperiodic electrical excitation to the surface of the cylindricalpiezoelectric transducer such that resonant acoustic waves are generatedin the volume between the cylindrical piezoelectric transducer and therigid cylinder; and (d) means for introducing the fluid having particlessuspended or entrained therein into the region of the equilibrium forcepattern formed by the resonant acoustic waves such that the particlesmove to the region of the equilibrium force pattern and are concentratedthereby.